Least Common Multiple (LCM) of 27 and 61
The least common multiple (LCM) of 27 and 61 is 1647.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 27 and 61?
First, calculate the GCD of 27 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 61 = 0 remainder 27 |
| 2 | 61 ÷ 27 = 2 remainder 7 |
| 3 | 27 ÷ 7 = 3 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 22 | 2310 |
| 148 and 176 | 6512 |
| 11 and 36 | 396 |
| 159 and 200 | 31800 |
| 165 and 71 | 11715 |